Recently, as the active elements in semiconductor integrated circuits have become smaller in size, corresponding improvements in the resolution of projection-exposure (projection-microlithography) methods used for imprinting active elements have been required. The relentless demand for achieving ever-finer pattern resolution in projection-microlithography has revealed the resolution limits (dictated by limits of light diffraction) of current projection-microlithography methods that employ deep-UV light. Consequently, substantial effort currently is underway to develop a practical projection-microlithography apparatus that employs “soft X-ray” (also termed “extreme ultraviolet” or “EUV”) light having a wavelength of 11 to 14 nm. See, e.g. Tichenor, et al., Proceedings SPIE 2437:292(1995). As referred to herein, this new microlithography method is termed “EUV Lithography” (abbreviated EUVL). EUVL is expected to achieve a pattern resolution of 70 nm or less, which is currently impossible using conventional lithography methods (ultilizing deep-UV wavelengths of 190 nm or more).
Since the refractive indices of known materials are nearly unity (1.00) in the EUV wavelength band, ordinary optical elements for refraction or reflection cannot by employed. Instead, grazing-incidence mirrors can be used that exploit total reflection from a surface of a material having a refractive index slightly less than 1. Alternatively, multi-layer-film reflection mirrors can be used in which weak rays of EUV light are reflected from the interfaces of multiple, superposed thin layers formed on the surface of a mirror substrate. The reflections from the interfaces are in phase with each other and cooperate to yield a summed high reflectivity. An exemplary conventional multi-layer-film reflection mirror has a surficial multi-layer film that comprises alternating layers of molybdenum (Mo) and silicon (Si). Such a multi-layer film exhibits a reflectivity of 67.5% at a wavelength band in the vicinity of 13.4 nm for perpendicular incidence. Another conventional multi-layer-film mirror has a multi-layer film that comprises alternating layers of Mo and beryllium (Be). Such a multi-layer film exhibits a reflectivity of 70.2% at a wavelength band in the vicinity of 11.3 nm for perpendicular incidence. See e.g., Montcalm, Proceedings SPIE 3331:42(1998).
A conventional EUVL apparatus comprises a soft X-ray source, an illumination-optical system, a mask stage, a focusing—optical system (projection-optical system), and a wafer stage. The soft X-ray source can be a laser-plasma light source, a discharge-plasma light source, a synchotrom-radiation light source, or the like. The illumination-optical system typically comprise multiple grazing-incidence mirrors that reflect a beam of soft X—ray light incident on the reflective surfaces of the mirrors from an oblique direction. The illumination-optical system also comprises one or more multi-layer film reflection mirrors as summarized above and a filter that transmits a soft X-ray beam having a predetermined wavelength. Soft X-ray light passing through the filter illuminated a photomask (reticle) that usually defines a pattern to be transferred to the wafer (lithographic substrate). Since substances that are transparent to soft X-ray light are currently unknown, the photomask must be a reflective mask rather than a transmissive photomask as used in conventional projection-microlithography. The pattern (e.g., for a circuit layer) defined on the reflective photomask is projected and focused onto the surface of a wafer or other suitable substrate, coated with a photoresist, by the focusing-optical system. To such end, the focusing-optical system comprises a plurality of multi-layer-film reflection mirrors. Since soft X-ray light is absorbed and attenuated in the atmosphere, all portions of the apparatus in which soft X-ray light is propagated are maintained at a predetermined vacuum (e.g., less than 1×10−5 Torr).
In the focusing—optical system, since the reflectivity of each of the multi-layer-film reflection mirrors is not 100%, it is desirable to minimize the number of multi-layer-film reflection mirrors so as to minimize the loss of light flux passing through the focusing-optical system. One exemplary conventional focusing-optical system comprises 4 multi-layer-film reflection mirrors (Jewell et al., U.S. Pat. No. 5,315,629; Jewell, U.S. Pat. No. 5,063,586). Another conventional focusing-optical system comprises 6 multi-layer-film reflection mirrors (Williamson, Japan Unexamined Patent Application No. Hei 9-211332; U.S. Pat. No. 5,815,310). Unlike a refractive optical system through which the luminous flux (pencil of rays) travels in one direction, reflective optical systems through which the luminous flux travels back and forth from one mirror to the next require that steps be taken to prevent shading the luminous flux by any of the mirrors. This constraint can make it difficult to increase the numerical aperture (NA) of the optical system. Conventional 4-mirror optical systems exhibit an NA of 0.015, and conventional 6-mirror optical systems have been made that exhibit a larger NA. Generally, the number of multi-layer-film mirrors is an even number to allow the mask stage and wafer stage to be situated on opposite sides of the focusing—optical system.
To provide satisfactory correction of aberrations in these reflective optical systems while using a limited number of multi-layer-film mirrors the surface of each of the multi-layer-film mirrors is machined to have an aspherical profile. Also, the illumination field is usually configured as a ring-field so as to provide aberration correction only near a predetermined image height. To transfer the entire pattern from the photomask to the wafer, exposure is carried out with the mask stage and wafer stage being scanned at certain respective velocities determined by the magnification of the focusing-optical system.
The focusing—optical system is a so—called a diffraction-limited optical system of which wave aberrations must be adequately reduced in order to obtain satisfactory performance from the system. An exemplary performance standard is an RMS (root means square) wave aberration no greater than λ/14, wherein λ is the wavelength of soft X-ray light with which the system is used. See, Born and Wolf, Principles of Optics, 4th edition, Pergamon Press, p. 469(1970). This is a condition at which Strehl intensity (a ratio of a maximum point intensity of an optical system exhibiting an aberration, compared to a stigmatic optical system) is 80% or greater. From practical standpoint, the focusing-optical system should exhibit an aberration of less than λ/14.
EUVL technology developed recently mainly utilizes a soft X-ray wavelength in the vicinity of 13 nm or 11 nm. The figure error (FE) allowable for each of the multi-layer-film reflection mirrors in the focusing-optical system is expressed as follows, as a function of wavefront error (WFE):FE=WFE/2/√{square root over (m)} (RMS)where m is the number of reflection mirrors in the optical system. The divisor of 2 reflects the fact that an error of 2 times the figure error is added to the wavefront error because both incident light and reflected light are affected by the figure error. Finally, in a diffraction-limited optical system, the figure error (FE) allowable for each reflection mirror is expressed by the following equation, where λ is the wavelength and m is the number of reflection mirrors:FE=λ/28/√{square root over (m)} (RMS)The FE at a wavelength of 13 nm is 0.23 nm (RMS) in the case of an optical system comprising four reflection mirrors, and is 0.19 nm (RMS) in the case of an optical system comprising six reflection mirrors.
It is very difficult to manufacture aspheric reflection mirrors having such high precision, which is the main reason why EUVL currently is not in practical use. Although the machining accuracy for an aspheric surface currently achievable is about 0.4 and 0.5 nm RMS (see Gwyn, Extreme Ultraviolet Lithography White Paper, EUVLLC, p. 17 (1998)), further improvements in the machining technique (and in measurement techniques) for aspherical surfaces are required to realize a practical EUVL apparatus.
Recently, Yamamoto reported a break-through technique that achieves sub-nm correction of the figure error of a multi-layer-film reflection mirror by scraping one or more individual layers from a selected region on the surface of the multi-layer-film reflection mirror. Yamamoto, 7th International Conference on Synchrotron Radiation Instrumentation, Berlin, Germany, POS 2-189, Aug. 21-25, 2000. The principle of this scraping technique is explained with reference to FIGS., 8A-8B, depicting a mirror of which the multi-layer-film is made of respective layers of two types of substances, A and B, wherein the layers are deposited alternatingly in a superposed manner, with a period length of d (FIG. 8A). To achieve correction, at least one layer pair is scraped off in a selected region, as shown in FIG. 8B. In FIG. 8A, the optical-path length of one layer pair having a combined thickness of d along a light-beam trajectory that is perpendicularly incident to the surface of the multi-layer film is expressed by OP=nAdA+nBdB, wherein dA and dB are the respective thickness of layers A and B, respectively, and dA=dB=d. Also, nA and nB are the respective refractive indices of the substances A and B. As shown in FIG. 8B, the optical-path length of a region having a thickness of d, in which one layer pair is scraped from the uppermost surface of the multi-layer-film, is expressed by OP′=nd, wherein n is the refractive index in vacuum (n=1). Accordingly, the optical-path length of a light beam incident to the scraped region is varied by scraping one or more of the uppermost layers from the multi-layer film. This is optically equivalent to modifying the surface shape of the multi-layer film by varying the optical-path length. The variation in the optical-path length (i.e., the variation in surface shape) is expressed by Δ=OP′−OP. Since the refractive index of known substances is essentially unity (1) in the wavelength band of soft X-rays, Δ has a small value. Consequently, the surface shape can be precisely corrected using this method. For instance, consider a multi-layer-film mirror comprising alternating layers of Mo and Si, used at a wavelength of 13.4 nm. For perpendicular incidence, d=6.8 nm, dMo=2.3 nm, and dSi=4.5 nm. In this wavelength band, the refractive index (nMo) of Mo is 0,92 and the refractive index (NSi) of Si is 0.998. Calculating the variation in optical-path length using these values, OP is 6.6 nm, OP′ is6.8 nm, and Δ is 0.2 nm. By scraping one layer pair having a thickness of 6.8 nm the surface shape can be modified within an accuracy of 0.2 nm. Incidentally, in the case of Mo/Si multi-layer film, since the refractive index of the Si layer is nearly 1, the variation in the optical-path length is mainly dependent on the existence or non-existence of the Mo layer and thus is independent of the existence or non-existence of the Si layer. Accordingly, while scraping the uppermost layer from the multi-layer film it is unnecessary to control the thickness of the Si layer precisely. In this case, the thickness of the Si layer is 4.5 nm, and scraping can be stopped at any depth through the Si layer. In other words, processing at an accuracy of several nm yields a correction of the surface within about 0.2 nm.
From a practical perspective, a reflective wavefront produced by a multi-layer-film mirror is measured after forming the multi-layer film. Reflectivity reaches a maximum (“saturates”) at a particular number of layers, and exhibits no further increase with additional layers. Whenever the number of layers is sufficient to achieve a saturated reflectivity, reflectivity does not change even if one or several layers of the multi-layer film are scraped away.
In general, a multi-layer film has a certain internal stress. Consequently, a Mo/Si multi-layer film or a Mo/Be multi-layer film used on an EUVL reflection mirror tends to exhibit a certain internal stress. For instance, it has been reported that a Mo/Si multi-layer film has a compressive stress of about −450 MPa, and a Mo/Be multi-layer film has a tensile stress of about +400 MPa. Mirkarimi et al., Proceedings SPIE 3331:133-148 (1998). In EUVL, the internal stress in a multi-layer film of a mirror in the focusing-optical system can substantially influence the shape of the substrate surface on which the multi-layer film is formed.
As described above, the shape accuracy required of the reflection mirrors used in the focusing-optical system used for EUVL is 0.23 to 0.19 nm RMS or less. Even if the mirror substrate for such a mirror can be processed to have sluch an accurately formed surface shape, whenever a conventional Mo/Si multi-layer film or Mo/Be multi-layer film is formed on the shaped surface of the mirror substrate, the shaped surface of the substrate tends to be deformed due to the internal stress imposed by the multi-layer film. The magnitude of the deformation caused in this manner can substantially exceed the required shape accuracy.
For instance consider at Mo/Si multi-layer film (having a period length d=7.0 nm, Γ=0.35, and 50 layer pairs) exhibiting an internal stress of −400 MPa formed on a surface of a mirror substrate having a diameter of 200 mm and a thickness of 40 mm. Such a film can cause a substrate-surface deformation that exceeds 20 nm. (Here Γ is the ratio of the thickness of the layer of material exhibiting higher refractivity, relative to the period length. In this instance Γ is the ratio of thickness of a Mo layer to the period length of 7.0 nm.) The influence of the component, among the possible deformation components, causing the variation in the radius of curvature of the mirror substrate can be modulated by adjusting the distance between adjacent mirrors of the optical system while minimizing any adverse influence on imaging performance. However, it is impossible to modulate the distance between mirrors sufficiently to achieve a deformation component of 1 nm or more without substantially influencing the optical characteristics of the EUVL optical system. Hence, according to conventional thinking, the absolute value of stress in an multi-layer film should be suppressed to less than 50 MPa.
In order to solve this stress problem, methods for stress reduction in the multi-layer film have been proposed. One method involves forming a multi-layer-film unit configured as a Mo/Ru/Mo/Si multi-layer film rather than the conventional Mo/Si structure. After forming each Mo layer, an ion beam is irradiated on the surface of the newly formed Mo layer (Shiraishi et al., Proceeedings SPIE 3997:620-627 (2000)), and the substrate is heated while forming the film layers. The Shiraishi method yields a reduction to +14 MPa tensile stress in the multi-layer film.
In another method, a Mo/Be multi-layer film having a certain tensile stress is pre-formed in order to cancel the deformation caused by compressive stress in a Mo/Si multi-layer film, which results in a cancellation of stress after forming the multi-layer-film (Mirkarimi et al., Proceedings SPIE 3331:133-148 (1998)). In this method a multi-layer film is formed on a back surface of the mirror substrate to cancel the deformations in the multi-layer film formed on the “front” surface. Based on the deformation of the substrate caused by the stress of the multi-layer film on the front surface, the substrate is machined to a have a shape predicted as a target shape after the deformation caused by the multi-layer film on the front surface
Although the method for controlling the reflected wavefront proposed by Yamamoto et al. is useful, locally scraping the multi-layer film causes the thickness of the multi-layer film to become uneven on the surface of the mirror substrate. As described above, since most multi-layer films have internal stresses of about several hundred MPa in general, if a multi-layer film is locally scraped, the total stress (stress×thickness) in the multi-layer film before commencing scraping is different from the total stress after completing scraping. This change in stress causes a deformation in the substrate.
A conventional method for controlling the reflected wavefront by scraping the multi-layer film is shown in FIGS. 9A-9C. As shown in FIG. 9A, respective Mo/Si multi-layer films 91 and 95 are formed on the front and rear surfaces, respectively of a planar mirror substrate 93. As a result of forming the multi-layer films on both surfaces of the mirror substrate, the deformation caused by stress of the multi-layer film on one surface of the substrate is canceled by the deformation caused by the stress of the multi-layer film on the other surface of the substrate. Thus, the substrate shape is maintained as planar. Each Mo/Si multi-layer film is composed of 50 layer pairs having a period length d=6.8 nm, Γ=0.35, topped off with 10 layer pairs having d=6.8 nm and Γ=0.1. The multi-layer film is formed by ion-beam sputtering. Here Γ is the ratio of the Mo layer thickness to d. The upper 10 layer pairs, having Γ=0.1, serve to improve the accuracy with which the wavefront can be controlled by scraping layers. By scraping one layer pair from the surface of this multi-layer film, the optical-path length is lengthened by 0.5 nm, causing a corresponding delay of 0.1 nm in the reflected wavefront at both incidence and reflection (see above). As shown in FIG. 9B, scraping a region 97 from the multi-layer film allows the shape of the reflected wavefront to be controlled with high accuracy by adjusting the amount actually scraped away from the reflective surface. However, since the Mo/SI multi-layer film exhibits a compressive stress of −450 MPa, the thickness of the multi-layer film undergoing scraping becomes uneven. This causes the balance of a total stress (stress×thickness) on both surfaces of the substrate to the perturbed, which causes the shape of the substrate to become uneven, as shown in FIG. 9C. If a part of the Mo/Si multi-layer film is scraped off, the scraped film has a compressive stress; hence, the portion undergoing scraping is deformed to concave. As a result, the reflective surface exhibits a further delay to the wavefront by an amount that is greater than predicted by the actual scraping, which prevents the wavefront from being controlled with a desired accuracy.
The shape of the wavefront after locally scraping the multi-layer film depends not only on the change in the optical-path length of the reflective light actually caused by the scraping, as described above, but also on the deformation of the substrate caused by the resulting unevenness of the total stress of the multi-layer film. Accordingly, in order to achieve a desired accuracy in the shape of the reflected wavefront by locally scraping the multi-layer film, it is no longer sufficient simply to determine the scraping amount based on the change in the optical-path length of the reflected light by only scraping the multi-layer film.